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Article Diaf2020 Article CharacterizationAndFrequencyAn(1)

Applied Water Science (2020) 10:59
Characterization and frequency analysis of flooding solid flow
in semi‑arid zone: case of Mekerra catchment in the north‑west
of Algeria
M. Diaf1
· A. Hazzab1 · A. Yahiaoui2 · A. Belkendil3
Received: 20 December 2018 / Accepted: 23 December 2019 / Published online: 20 January 2020
© The Author(s) 2020
In this study, we evaluate the soil erosion and solid transport in the oued Mekerra watershed in north-west Algeria. The
study area is subject to a semi-arid climate characterized by irregular rainfall and showers, which are often accompanied
by significant floods. These floods of large volumes transport large amounts of solid input to the Sarno dam, which is in
the outlet of oued Mekerra. Therefore, the water storage capacity of this dam is gradually decreasing, and it might reach
the volume of dead water. For this study, we utilized the hydrometric database provided by the National Agency of Water
Resources (ANRH). The operating period was 24 years, from 1988 to 2012. This period was extended by classic regression
to 65 years, which allowed extracting a series of annual maximum instantaneous flow rates (QIXA) and subsequently quantified the sediment yield during floods. The specific degradation mean created by the 11 floods was quite high, in the order
of 20 t km2 year−1. The highest value of solid contribution was observed during the floods of October 2000 (250,000 t), and
the value of liquid contribution was 7,151,608 m3. The extracted results from the analysis of the graphs of concentration as a
function of the liquid flow (C = f′(Ql)) showed four types of hysteresis curves: clockwise loop, counterclockwise loop, shape
of eight, and straight line curve. Class II (clockwise loop) was the dominant class in the four events, namely the floods that
occurred on 09/22/1992, 09/21/1998, 09/27/1999, and the 08/24/2002. From these results, the water resource sector managers could formulate various methods for protection from floods and against the risk of sedimentation in storage structures.
Keywords Solid transport · Oued Mekerra · Semi-arid · Sediment concentration · Liquid flow
Electronic supplementary material The online version of this
article (https​://​1-019-1132-4) contains
supplementary material, which is available to authorized users.
* M. Diaf
[email protected]
A. Hazzab
[email protected]
A. Yahiaoui
[email protected]
A. Belkendil
[email protected]
Modeling and Computational Methods Laboratory,
University Dr. Moulay Tahar of Saïda, P.O. Box 138,
20000 En‑Nasr, Saïda, Algeria
Department of Civil and Hydraulic Engineering, Faculty
of Technology, University of Tahri Mohammed in Bechar,
P.O. Box 417, 08000 Béchar, Algeria
Laboratory 60: Water Resources Valorisation, Science
and Technology Faculty, University Abou-Bekr Belkaid
of Tlemcen, P.O.Box 119, 13000 Tlemcen, Algeria
Owing to its geographical location and climate regime,
Algeria remains severely limited in terms of water resources.
The volume of water lost by siltation in the dams is recognized as one of the main problems of the country.
The phenomenon of loss of water is growing and threatens more than 20 Algerian dams (Remini and Mokeddem
2018). The effect of erosion is not limited to the siltation of
dams, but it also deals with major problems such as degradation of fertile land, water quality, and the destabilization of
hydraulic structures.
The occurrence of flood is conditioned by the intensity
and quantity of the rainfall. The flow rate of each flood event
depends essentially on several hydrological and morphological parameters, such as drainage density, slope, compactness
index, and the confluence ratio (Pallard et al. 2009; Yles and
Bouanani 2016). The high speed of the flow causes detachment of soil particles from the bulk soil mass, which might
59 Page 2 of 15
lead to transport of detached sediments (Hajigholizadeh
et al. 2018).
In Algeria, the specific erosion rate reaches considerable values, which exceeds ­103 t km−2 year−1. It reaches up
to 1120 t km−2 year−1 in the High Tafna (Megnounif et al.
2004), 1330 t km−2 year−1 in the Tafna sub-basin (Ghenim
et al. 2008), and 1875 t km−2 year−1 in the Chelif sub-basin
(Meddi 1999). The watershed of the oued Mekerra contributes to the siltation in the Sarno dam (commissioned in
1954), resulting in a significant amount of suspended solids
in the dam.
The main objective of the solid transport data analysis
is to determine the origin of the transported sediments,
through the analysis of concentration curves as a function
of flow rates (C = f(Q)). Several studies have focused on the
study of transport and quantification of solids (Nones 2019;
Mrokowska and Rowinski 2019; Di Francesco et al. 2016;
Tabarestani and Zarrati 2015; Vrolix and Pissart 1990). In
Algeria, several researchers have evaluated the sediment
transport associated with the floods in the country. A few
examples include the studies done for the watershed region
of the Tafna river in the north-west Algeria (Bouchelkia
et al. 2011; Ghenim et al. 2007; Megnounif et al. 2004; Terfous et al. 2001) and for the region of Wahrane watershed
(Benkhaled and Remini 2003).
The diversity of relationships between liquid and solid
flows as a function of spatial and temporal disparity interested several researchers to carry out probability modelling
using frequency analysis for western Algeria (Yahiaoui and
Touaibia 2011), the eastern Algerian watersheds (Mouas and
Souag 2017), and the Walloon region of Belgium (Dautrebande et al. 2006). The hysteresis graph is one of the methods used to analyse sediment concentration as a function of
flow rates (C–Q) (Pagano et al. 2019; Sadeghi et al. 2018;
Zhao et al. 2017; Lloyd et al. 2016). Williams (1989) is
the first to categorize the hysteresis according to the shape
of each graph into five classes: clockwise loop, counterclockwise loop, eight loops, straight line, and complex
loop (Hamshaw et al. 2019). Hysteresis classes are used to
identify physical processes in the watersheds. For example,
clockwise hysteresis indicates that the source of sediment
could be the outlet of the watershed, while counterclockwise
loop hysteresis indicates that the source of sediments is in
the headwaters (Delaney et al. 2018; Chalov et al. 2017;
Baca 2008).
The dam of Sarno was built between 1947 and 1954 in
the outlet of the oued Mekerra watershed. At commissioning, it had a theoretical starting capacity of about 22 Mm3.
oued Mekerra contributes to the silting of the dam of Sarno
by an average specific degradation of about 38 t km2 year−1
(Cherif et al. 2017). To put forward a better strategy to fight
against this problem, it is necessary to have a precise understanding of the variations in the sedimentation rates during
Applied Water Science (2020) 10:59
each hydro-rainfall period. The determination on erosion
rate is based on the graphical analysis of the hysteresis
traced according to the relation Qs = f(Ql). The classification proposed by Williams (1989) of the different loops of
hysteresis is adopted to determine the sources of origin of
the sediments.
Study area
The watershed of the oued Mekerra is a sub-basin of the
Macta watershed, mostly located in the Sidi-bel-Abbes
region in western Algeria. It is about 400 km west of Algiers
(between 1°–0° 30′ W and 34° 20′–35° 15′ N). The basin
is limited to the north by the Tessala mountain range, to
the south by the highlands (Ras El Maa), to the east by the
Telagh plateau and the Saïda Mountains, and to the west by
the Tlemcen Mountains (Fig. 1).
The main stream of oued Mekerra has its origin in the
high valleys; it drains an area of about 3000 km2 and has a
course of 125 km and an average slope of 5.5%, a perimeter
of 280 km with a compactness coefficient of 1.43 that reflects
well the elongated shape of the watershed. The elevation of
mountain ranges is 1000–1100 m in the north, 1200 m in
the west, 1200–1260 m in the south, and 870–1460 m in the
east. 48% of the watershed is located above 1000 m above
sea level.
The oued Mekerra crosses two zones of very distinct
reliefs, the Daya mountainous massif in the south, with
an altitude between 800 and 1600 m, and the plain of the
Mekerra, where the city of Sidi-bel-Abbes is located, in
the north, with an average altitude of 550 m. The Mekerra
watershed is a result of drainage of several small streams and
tributaries. In the south, there are the El Kheoua, Sekhana,
El-Lellelah, Ras El Ouiden, and Farat Ezziet streams. In the
south-west are the Et-Touifza and Tadjmout streams and in
the north-west are the Lemtar, Bukhenafis, Anefress, and
Tissaf streams. All these streams contribute to the oued
Mekerra as the main stream in the catchment. It has its
source in the south at an altitude of 1100 m and crosses
the city of Sidi-bel-Abbes at an average altitude of 500 m,
with an average slope of about 1%. The vegetal cover in the
watershed is irregularly developed. Downstream from the
town of Ras El Ma appears Alfa covered land, which, to
the north, gives way to brush covered land. In the region of
Sidi Ali Benyoub, the Alfa gives way to cereals, vines, and
citrus fruits. About 20% of the basin area is forest-covered
(Otmane et al. 2018).
The following are some of the factors that favour the phenomenon of erosion in the Mekerra region:
• A well-defined hydrographic network with a drainage
density of 1.67 km km−2 and a torrential coefficient of
Fig. 1 Geographical location of the oued Mekerra catchment
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59 Page 4 of 15
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Fig. 3 Rainfall variation (1990–2003)
Fig. 2 Map of land cover of oued Mekerra catchment
0.23 indicates a torrential regime where the predominant soil erosion gives a very strong solid flow (Fig. 2).
• The prolongation of the dry period during several
months has destroyed the plant cover that characterizes as the main soil protector against the splash effect
(Benkhadra 1997).
• Only a part (20%) of the Macta watershed has forest
cover, consisting mainly of Aleppo pine and holm oak,
and hence provides a very weak protection against soil
erosion (Hallouche et al. 2017).
• The elongated shape of the watershed and the irregularities in the rainfall and the vegetation cover are linked
to the fragility of the soil
The oued Mekerra catchment is under the influence of a
semi-arid Mediterranean climate characterized by a hot
and dry summer and a relatively mild and humid winter. The prevailing winds are from the north-west and
west; the average maximum inter-annual velocity is about
20 m s −1 (Otmane et al. 2018). The temperature values
vary between a minimum value of 10 °C and a maximum
of 24 °C, with an annual average of 17 °C. The cold and
rainy period extends from the beginning of October until
the end of April, while the dry period starts from May
and last until September (Atallah et al. 2016). The evapotranspiration has an average value of 1670 mm year−1,
between a maximum of 1883 mm year−1 and a minimum
of 1588 mm year −1, resulting in the rapid drying up of
soils and the degradation of the vegetation cover. These
variations favour, in case of showers, the development of
a fast surface flow and significant erosion.
Data acquisition
The climatological data for the period from 1990 to 2003
were provided by the National Agency for Hydraulic
Resources (ANRH). The climatology of the watershed
gives an average yearly rainfall of 300 mm. During the
wet years, rainfall can reach up to 400 mm, and during
dry years, it can decrease to less than 200 mm (Fig. 3).
Fig. 4 Correlation of maximum solid flow as a function of maximum
liquid flow rates
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Fig. 5 The variability of solid
flows and maximum liquid
flows from 1942 to 2008 at the
Sidi-bel-Abbes station
The hydrometric series from the Sidi-bel-Abbes station
(station code—110301), which is located at the outlet of the
watershed (1° 00′–0° 30′ W; 34° 20′–35° 15′ N), extends
from January 1, 1988, to December 30, 2012, and includes
10,048 instantaneous data of liquid flow rates Ql ­(m3 s−1),
solid flow rates Qs (kg s−1), concentration of suspended matter (g l−1), and heights (cm).
These data are recorded every 2 days. During floods,
data survey is intensified up to 1 h or even 30-min time
intervals depending on the flow level. However, this series
has missing data gaps for the years 1997, 2004, 2005, and
2007. These deficiencies are corrected by applying classical regression in the form of (Qs= aQl − b). The method
used is a numerical method based on the application of a
classical regression model with the hydrometric series of
(1988–2012). The law of regression is deduced with a correlation coefficient of R = 0.87 (Fig. 4). The series considered was extended for a 65-year period from 1943 to 2008.
Extension of the period of study is justified by the need for
continuous observation series over a sufficiently long period
(Vrolix and Pissart 1990).
The analysis of the variation of the maximum flows
between the years from 1943 to 2008 (Fig. 5) gave two
dry periods that prolonged over the years 1947–1950 and
1955–1986. The other years were wet with the year 1994
recording 228 m3 s−1 of liquid flow and solid flow of
4030.86 kg s−1, along with suspended matter concentration
of 20 g l−1. The year 2008 recorded 183 m3 s−1 of liquid
flow and a significant solid flow of 3667.87 kg s−1, which
confirms the irregularity of the flow rates in the basin.
The extreme flow of floods occurs twice a year, one during
autumn (October and September) with maximum value reaching up to 200 m3 s−1 and another during spring, especially in
March and April, according to the cycles of annual flows from
the Sidi-bel-Abbes station. The torrential coefficient indicates
a torrential flow regime where soil erosion is predominant and
consequently a very strong solid flow. The stream flows in the
north of Algeria allow distinguishing two types of regimes: a
simple regime where the high waters occur in the cold season,
with a maximum between January and March, and the low
flows taking place in July–August. It characterizes the coastal
streams, and a complex regime with two annual maxima, more
or less marked, occurs in autumn and spring, the main low
water being in summer (Taibi et al. 1993); the latter characterizes the flow in the stream of oued Mekerra.
Table 1 The estimation of different solid–liquid contributions specific to the flood periods
P (mm)
H (cm)
C (g l−1)
QL ­(m3 s−1)
Qs (kg s−1)
AS ­(103 ton)
AL ­(104 m3)
ASS (t km−2)
16-Sept 97
The mean
P precipitation, H height, C concentration, QL liquid flow, Qs solid flow, AS solid input, AL liquid intake, ASS specific solid input
59 Page 6 of 15
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Table 2 Classes of C–Ql relations (Williams 1989)
Criterion C/Ql
Single line, straight line
Curve, the slope increases when QL increases
Curve, the slope decreases when QL increases
Clockwise loop
Counterclockwise loop
Single line plus a loop
Form in eight (8)
(C/QL)m = (C/QL)d. The slopes of the two sections (rise and
recessional) are equal
The slopes of the two sections (rise and recessional) are unequal
The slopes of the two sections (rise and recessional) are unequal
(C/Ql)m > (C/Ql)d. For all QL values
(C/Ql)m < (C/Ql)d. For all QL values
(C/Ql)m = (C/Ql)d. For some of the values of QL
(C/Ql)m > < (C/Ql)d. For the other part of QL values
(C/Ql)m > (C/Ql)d. For some of the values of QL
(C/Ql)m < (C/Ql)d. For the other part of QL values
Characterization of solid transport
Frequency analysis of solid flow
Generally, suspended flow Qs is related to liquid flow rates Ql
(Wood 1977; Walling and Webb 1981; Walling 1983; Etchanchu and Probst 1986) by the following equation:
Extreme flows are responsible for the damage caused by
floods (Henstra and Thistlethwaite 2017). It is interesting to
model the extremes of flows using a frequency analysis. The
purpose of the analysis is to determine quantiles based on
the return period (Botero and Francés 2010). The series of
extreme solid flows has a sufficient size of 43 values and has
the empirical characteristics presented in Table 3 to perform
the adjustment of a statistical law.
The quality of the sample is verified using several statistical tests proposed in previous studies (Wald 1943; Mann
and Whitney 1947; Grubbs and Beck 1972; Forthofer and
Lehnen 1981), to test the independence stationarity, homogeneity, and singularity of the sample. The decision support
system identifies the most appropriate class for adjusting a
flow sample and estimating the QT quantile of high return
period (Ouarda et al. 1994; El Adlouni et al. 2008; Yahiaoui
and Touaibia 2011). The methods developed in this system
allow identifying the most suitable class for a series adjustment. These methods are as follows:
Qs = c × Ql
Ql is measured in ­m3 s−1, Qs in kg s−1 and C the concentration in g l−1.
Solid flows (As) are calculated by the following formula:
As =
(ti+1 − ti ) × (Qi × Ci ) × 10−3
(ti+1 − ti) being the time duration between two successive
withdrawals, where ti is the time corresponding to the flow
rate and n is the number of withdrawals. The specific inputs
(ASS) tonne per square kilometre per year are:
Ass = As × 106 ∕A
where A is the area of the catchment area in ­km2.
Liquid inputs (Al) in ­m3 are calculated by:
Al =
(ti+1 − ti ) × Qi
• The log–log graph used to differentiate between classes
For the period from 1980 to 2012, we obtained 11 floods,
which are represented in Table 1.
To understand the solid transport mechanism and its origin, it is necessary to study the relation between the concentration C (g l−1) and the liquid flow Ql (Williams 1989). The
classification of the models from the analysis of the concentration and liquid flow curves C − Ql is given in Table 2.
The fundamental relationship of the concentration as a
function of the liquid flow is illustrated in Fig. 6, in the
form of hysteresis, for the eleven floods that occurred during 1989–2008.
C (distributions with regular variations), D (sub-exponential distributions), and E (exponential law);
• The average function of excesses (FME), used to differentiate classes D and E; and
• Two statistical methods: Hill’s report and Jackson’s
statistics that could be used to perform a confirmatory
analysis of suggested conclusions from the two previous
consists of the adjustment of the series
( The log–log diagram
x1 , x2 , … , xn to the power law of Pareto or Zipf whose
probability density function is:
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Fig. 6 The variation of the concentration as a function of the liquid flow rates in the form of hysteresis
59 Page 8 of 15
Fig. 6 (continued)
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Fig. 6 (continued)
Table 3 The empirical characteristics of the solid flow series
Standard deviation
kg s−1
kg s−1
kg s−1
P(X = x) = k
where k and xmin are the parameters of form and scale of the
Pareto law. In the case of oued Mekerra and by the method
of moments, I = 2.4 and xmin = 565 kg s−1.
The graphical adjustment of the QIX solid series to the
power distribution can be an exponential distribution (class
E) or one of the class D distributions.
59 Page 10 of 15
The average function of the excesses is constant for an
exponential distribution of the scale parameter a (e(u) = a).
The e(u) varies around an average of 13.3 m3 s−1, between the
two extremes 12.4 and 0.89 m3 s−1, which leads to adjusting
the QIX solid series to the exponential law (class E).
Relationship between suspended matter (MES)
flows and hydrological conditions
According to the morphometric data of the watershed, it
is possible to distinguish the factors that favour erosion in
the Mekerra region as well as the elongated shape of the
watershed, irregular rainfall, and a weak vegetation cover
(Benkhadra 1997, Hallouche et al. 2017). The thermal regime
may increase evapotranspiration, rapid soil drying, and degradation of vegetation cover. These variations favour, in case of
showers, the development of rapid surface flow and significant
Relationship between flow and climatological
Annual maximum flow rates have generally been observed
in autumn (October and September) with a value of up to
200 m3 s−1 and another in the spring of March and April.
According to Taibi et al. (1993), stream flows in northern
Algeria have two types of regimes, a simple regime and
a complex regime; the complex regime with almost two
annual maxima, occurring in autumn and spring and the
main low water occurring in summer. This characterizes the
flow of our current oued Mekerra.
The analysis of the variations of maximum flows during
the period 1942–2008 gave two prolonged dry periods: from
the years 1947 to 1950 and from 1955 to 1986. The other
years are wet, among which the most important years are
2000 and 2008, which confirms the irregularity of flows in
the basin. The succession of years with light humidity or
drought has led either to a considerable accumulation of
water supply or to a latent drought. As shown in Table 1,
floods occurred even when rainfall was very low, which indicates that rainfall has no influence on the floods (Ramírez
2000). These floods were usually recorded during autumn
(September and October), with the exception of those
recorded in August 1997 and April 1992 with high flow
rates and concentrations. The flood of 2008 with a maximum
water height of 445 cm, that lasted for 4 days (from October
25 to October 28, 2008), was the largest flood that occurred
during the study period, with a strong flow of 3668 kg s−1
and a liquid flow rate of 183 m3 s−1.
Abundant rainfall of exceptionally long duration lasted all
night (from October 23 to October 24, 2000), and the volume
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of rain received on the Ras El Ma heights was estimated to
be 100 mm of water. The consequences of this storm were
strongly felt by the population, who were surprised by the
flow of water arriving in the plain with a maximum flow
close to 200 m3 s−1 and a significant solid flow estimated at
10,517 kg s−1, depositing tons of sand and materials in the
streets and squares of downtown Sidi-bel-Abbés on its way.
Analysis of the 11 floods for the period 1980–2012 shows
that they occurred mostly in autumn (September and October) with a frequency of 72%, causing high specific soil degradation of 177 t km−2. In summer (August), they caused a
degradation of 42 t km−2, and in spring (9% of frequency)
a minimal value of 1 t km−2 was recorded. The total solid
specific degradation during the 11 floods was estimated to
be 220 t km−2, which is estimated as half that of the oued
Boumessaoud (541 t km−2) located in north-west Algeria
(Bouguerra et al. 2016).
As a comparison, the solid contribution of the oued
Mekerra during the flood period is 250,000 t (the maximum
value in floods), and it is superior to that of certain zones
forming part of the same semi-arid region, such as the watershed of oued Saida (9261 t), and lower than that of high
Tafna watershed (2,686,000 t).
Table 2 shows that the variation of the solid flows has a
relative relation with the liquid flow, with the exception of
some cases; for example (October 24, 2000) where we found
that the increasing fluid flow causes a solid flow decline due
to the draining of the aquifers coming from a large flood
(August 24, 2002).
Relationship between concentration and flows
by hysteresis
The hysteresis analysis shows that the oued Mekerra is subject to four classifications: Class II (clockwise loop) is the
dominant class in the four events, namely the 09/22/1992,
09/21/1998, 09/27/1999 and the 08/24/2002 floods (Fig. 6
(C-1 and C-2) (G-1 and G-2) (H-1 and H-2) (J-1 and J-2)).
Class II dominance indicates that the sediments have a
source close to the outlet of the watercourse either at the
bottom or in the areas surrounding the outlet (RodríguezBlanco et al. 2010; Alexandrov et al. 2007).
Another interpretation shows that the class II relation
indicates strong rain intensity at the beginning of the flood.
The time of arrival of flood explains the cause of the high
concentration of sediment. These floods occur during the
transition period between the end of the dry season (summer) and the beginning of the rainy season (autumn), and the
rainfalls on very dry ground without plant cover. This accelerates the appearance of a “splash” phenomenon (instantaneous erosion that causes the dissociation of soil particles). Generally, one can distinguish the class II hysteresis
from the graph of C/Q, where the sediment concentration
Applied Water Science (2020) 10:59
peak appears just before the liquid flow peak. According
to Arnborg et al. (1962), high concentration of sediment is
the index of existence of a pavement layer formed on the
streambed. This layer is created by a vertical deposit of the
soil particles according to the size of the elements, which
play a bed stabilizer role; some rocks are detached under the
strong floods effect by releasing the materials in suspension.
The concentration/flow relationship is of class III (counterclockwise loop) and is the second dominant class in the
studied floods series, where we can distinguish this relationship in the 11/13/1993, 08/27/1997, and 10/26/2008 floods
(Fig. 6 (D-1 and D-2) (E-1 and E-2) (K-1 and K-2)). The
graph shows that the maximum concentration is recorded
after the liquid flow rates reach their maximum (Mokadmi
2012). According to Williams (1989), the concentration values during the rising are lower than the liquid flow values
during the recession (C/Q(rising) < C/Q(recession)). Floods of
this relationship type were characterized by high rainfall and
relatively free run-off from the solid particles, as most of the
sediments were transported by the first floods of fall season.
Tananaev (2015) and Mokadmi (2012) cited three causes for
manifestation of this relationship (counterclockwise loop):
one of the main causes is the significant soil erodibility at
the same time as the prolonged erosion during the flood
(Megnounif et al. 2013). Another cause is the irregularity
in rainfall during the season, which has a direct influence on
the sediment production in the watershed (Benkhaled and
Remini 2003). The third cause is the shift between the flood
wave that affects the water bodies and the slower transport
of materials produced from the streams.
The class V hysteresis (shape of eight) combines two relations: that of a clockwise loop and its opposite, which is a
counterclockwise loop (Benkhaled and Remini 2003). This
form of hysteresis was recorded in two hydrological events:
the 09/18/1989 flood and that of 04/10/1992 (Fig. 6 (A-1 and
Page 11 of 15 59
A-2) (B-1 and B-2)). The first floods are positioned in the
transition phase between the end of summer and the beginning of autumn (beginning of rainfall). According to the
concentration/flow curves, the concentration peaks appear
before the flow by forming a loop in the clockwise direction. During the recession, the peak concentration begins to
decrease slightly relative to the liquid flow; this will form a
loop in the counterclockwise direction. The possible explanation for this relationship at this time could be that the year
1989 was a hydrological wet year, which helped recharging
of the aquifer to saturation by facilitating surface run-off and
recorded large liquid and solid flow values at the beginning
of the flood season (El Mahi et al. 2012). The second flood
was recorded in the spring season; this period of the year
is characterized by very high saturation of the soil after the
heavy rains in winter season, which explains the accentuation of superficial run-off and large values of liquid and solid
flow in the first moments of the flood.
The marked third relation is that of class I (simple curve
or straight line), observed for the flood that occurred on
October 24, 2000 (Fig. 6 (I-1 and I-2)). According to Williams (1989), the values of the concentration during the rising are equal to the liquid flow values during the recession
(C/Q(rising) = C/Q(recession)). The variation of suspended solids is
directly related to the flow of water (Megnounif et al. 2013).
This curve, of linear shape, indicates a strong relationship
between suspended sediment concentration and liquid flow with
uninterrupted supply throughout the flood; the main source of
suspended matter comes from dragging soil particles from
stream beds according to soil particle sizes (Hudson 2003).
The flood that occurred on September 16, 1997, is
assessed to be a complex flood (Fig. 6 (F-1 and F-2)). The
complexity of this kind of flood comes from the succession
of the floods in a short period, which contributes to the sudden increase in liquid flow values in the recession phase of
Fig. 7 Fitting and confidence
limits at 95% of the QIX_solid
series to the exponential distribution
59 Page 12 of 15
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the previous flood in an irregular way. Liquid inputs and
solid inputs are highly variable during the flood years.
Quantiles determining according to the return
period using the frequency analysis
With the objective of assessing the risks of floods in
future, a frequency analysis is applied using the adjustment of the Q IX solid flow series of the oued Mekerra
to an exponential distribution (Fig. 7) by the method of
moments that leads to the estimation of the scale parameter a = 972.21 kg s−1 from the function of the distribution
not exceeding:
( )
P(X ≤ x) = 1 − exp −
After estimating the distribution parameter, a fit test
consists in defining a decision rule concerning the validity
of the hypothesis concerning the agreement of an empirical distribution with theoretical distribution adjusted to
observations; the three fit tests are applied:
• For the Kolmogorov–Smirnov test, the observed value is
Dob = 0.121 and the theoretical value for a level of significance 𝛼 = 5% is Dth = 0.2074, the fit test is accepted
for Dob < Dth
• The production possibilities curve (PPC) coefficient test,
which reflects the correlation between the observed and
theoretical values of the same experimental frequencies,
is accepted for PPC = 0.992 which is close to 1.
• The root-mean-square deviation (RMSD) test, which
expresses the quadratic relative error, is equal to 0.3 and
is strictly less than 1. So the good-fit test is accepted.
Therefore, quantiles and corresponding confidence
intervals for a significance level 𝛼 = 5% are summarized in
Table 4.
Table 4 Quantiles and confidence intervals estimated by the exponential law
T (years)
Frequency of not
exceeding “p”
(kg s−1)
interval (95%)
The series of solid flows were subjected to a static
treatment that gave periodic flood flows. The flow values
increased depending on the period of return. For a 95% confidence interval, we have for every 2 years a flood of solid
flow equal to 674 kg s−1.
The solid flows QIXT_Solide in table 4 provide values that exceed the average value of the eleven (11) floods
(2256.5 kg s−1) for the periods after 50 and 100 years, and
even millennia which seem significant of 6716 kg s−1. Findings from earlier works show that:
The series of maximum flow for northern Algeria generally fits the Gumbel distribution and the log-normal law that
estimates values of flood flows from 1000 years (Hallouche
et al. 2017).
The normal log distribution is most appropriate for the
humid region, and the exponential distribution is preferable
for the semi-arid and arid regions (Mouas and Souag. 2017).
• The stations at the north-west Algerian watershed belong
to the class “D” of the sub-exponential distributions
(Meddi and Abbes 2014).
• The results of the statistical adjustment to the Mejjate
plain of Morocco (Boukhari et al. 2008) show that the
series of observations are well correlated with laws of
the logarithmic type (Pearson V) or exponential (Galton),
with test values ranging from 0.7 to 3. The normal law,
meanwhile, has high-test values.
The specific degradation for the 11 floods varies between
1 and 83 t km−2. The flow regime of the oued Mekerra is
complex with two annual maxima; one that occurred in
autumn (September 22) and other in spring (April 10) in
the year 1992.
Among the causes favouring soil erosion in the Mekerra
region are the irregularities in the rainfall and the vegetation cover, which consequently lead to significant flow.
The liquid and solid flow rates are strongly correlated
with a correlation coefficient R = 0.87. This obtained
relation gave an extension of the flows up to 65 years.
Statistical estimation of extreme flows using the annual
maxima method for the data yielded 11 floods. The specific degradation for the 11 floods is estimated between 1
and 83 t km2 year−1. The stream flow regime is complex
with two more or less marked annual maxima occurring
in autumn (September 22) and spring (April 10) of the
same year 1992.
The evolution of the concentrations as a function of the
liquid flows, during the 11 floods, was subjected to four
models; the most dominant is class II in the four events
Applied Water Science (2020) 10:59
(09/22/1992, 09/21/1998, 09/27/1999 and 08/24/2002),
which indicated high intensity of rainfall at the beginning
of the flood. The arrival time of these floods explains
the cause of high concentration of sediments. Class III
(counterclockwise loop) is the second dominant class
in the flood series (those of 11/13/1993, 08/27/1997
and 10/26/2008), and the maximum concentration was
recorded after the liquid flows reached their maximum.
Floods of this type are characterized by strong rainfall and
run-off that is relatively free of solid particles. The hysteresis of class V (shape of eight) combines two relations:
that of a loop in the clockwise direction and its opposite.
This form of hysteresis was recorded in two hydrological events: the floods that occurred on 09/18/1989 and
04/10/1992. Class I (simple curve or straight line) relation
was observed for the flood on 10/24/2000. According to
Williams (1989), the values of the concentration during
the rising are equal to the liquid flow values during the
recession C/Q(rising) ≈ C/Q(recession).
The modelling of extreme flow events was performed
by frequency analysis using the extreme flow data of the
floods responsible of damages. The purpose of the analysis was to determine quantiles based on the return period.
For the rare and stronger floods, it was possible to know
the decennial, fiftieth, and centennial frequencies with
the respective quantiles: 2239 kg s −1, 3803 kg s −1, and
4477 kg s−1.
Acknowledgements The authors would like to thank the Regional
Director of the ANRH in the Wilaya of Oran, for having made available all the necessary data to accomplish this work. We would like to
acknowledge the contribution of Mr. Baghli Abderrazak, Professor at
the University of Tlemcen, in writing this article, my thanks to Editing
(www.editag​ for the English edition. We would also like to thank
the reviewers for reading and editing this article. Their comments and
suggestions have improved the quality of this work.
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